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Quick Check 22.4 – Data 100, Summer 2020
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* Indicates required question
Are the vectors [1/2, 1/5] and [-1/2, 5/4] orthogonal, orthonormal, or neither?
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Orthogonal
Orthonormal
Neither
Let X be an n by p matrix of rank r, r < p. Suppose we take the SVD of X such that X=U @ Sigma @ V^T. Which of the following statements are true?
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The diagonal entries of Sigma are non-negative
U and V are orthogonal matrices
The r^th singular value is positive
The off-diagonal entries of Sigma are all 0
Required
If Q is an m x m square matrix and Q^T @ Q = I, which of the following are possible? Note that I is the identity matrix of size m x m.
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Q is an identity matrix
The columns of Q form an orthonormal set
Neither
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